There are a couple spec miata rentals:
http://larryoka.com/
http://www.aracing.org/
I rent a spec miata for a track weekend with Al at A+ racing and it was a great experience. It is pricey but given no choice (my car wasn't ready at the time) it is really worth it. Miatas don't have TCS so just get used to the car and you will be fine.